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CHAPTER 1: Understanding the Simplicity ... > Rates, Compounding, and Time Value - Pg. 3

Understanding the Simplicity of Valuation 3 RATES, COMPOUNDING, AND TIME VALUE Interest rates have an obvious impact on time value. If instead of 5 percent you were able to invest at 10 percent per year, your annual return doubles. One hundred dollars at 10 percent is worth $110 in a year and $121 in two years. At the end of five years it is worth $161, compared to $127 at 5 percent. The calculation of reinvested interest plus principal over a number of years is called compounding. The compounding of interest results in ever growing returns over time with the impact of interest rates magnifying over time. While the difference between 5 percent and 10 percent for a year might not seem like much, over five years the initial investment would have grown just 27 percent at 5 percent, while growing 61 percent at a 10 percent annual rate. After 10 years at 5 percent the original $100 will have grown to just $163, while the investment of $100 at 10 percent will have grown to $259. Just as future value increases with the discount rate, present value decreases. The present value of $100 paid in five years at 5 percent is $78.35, while the present value at 10% is just $62.09. The higher the discount rate, the less that future dollar is worth. We can see this in the equations. Since FV = PV × (1 + C) n , the larger the discount rate (C) and the longer it is invested in years (n), the more it